Electrical – Geiger Muller Counter capacitors voltage

The GM tube's voltage is important. You don't want to exceed it's maximum specification and also its sensitivity depends upon the voltage applied. And this may vary from GM tube to GM tube, so some ability to adjust the exact applied voltage would be a "nice to have" here. But it isn't included.

Regulation is therefore important. This circuit includes that regulation by feedback to pin 5 of the MC34063, with \$R_3\$, \$R_4\$ and \$R_5\$ forming the divider network. If all the resistor values were perfectly accurate, this would suggest about \$400\:\textrm{V}\$ across \$C_4\$. But \$10\:\textrm{M}\$ resistors are relatively hard to get, somewhat more expensive perhaps, typically only specified for about \$200\:\textrm{V}\$ or so, and otherwise may have worse specs. Expect to pay a few dollars for a 1% one rated for this voltage area. Even with all resistor values at 1% spec, the voltage at the output will be somewhere between \$385\:\textrm{V}\$ and \$425\:\textrm{V}\$. (Which I may consider "good enough", depending on the GM tube's specs.)

When I built one of these in 1969, we didn't have quite so fancy of regulators nor were our resistors well specified. I used a series chain of hand-selected NE-2's in order to set the regulation voltage and arranged the power supply so that the NE-2's had the appropriate current through them for reasonable regulation. It wasn't any more precise than this, but my voltage was set close to \$1200\:\textrm{V}\$ back then, too, because of the GM tube I used. (I actually wrote to the physicist who designed the tube and about 10 years later bought a new replacement from him directly, as no one was carrying them anymore. Cost me $8 in 1980. Nice.)

So \$C_4\$ is your main concern, since it must charge up to this maximum voltage. If you'd bothered to read the schematic you provided, you'd see the rating present on the schematic, directly. That's a good choice value.

When looking at the other capacitors, you only need to have a very general knowledge. For example, all you need to do is look at the MC34063 datasheet to see that pin 5 is \$1.25\:\textrm{V}\$ (with error bars, of course.) So you already know because also of the resistive divider next to \$C_3\$ that it won't be exposed much. Note however, that a single failure in either \$R_3\$ or in \$R_4\$ (say, broken by the accidental application of a pliers or screwdriver) would in fact expose a lot of parts to a high voltage probably killing them also (including the MC34063.) I think a redesign of this circuit would be appropriate because of that weakness. Stuff happens, you know?

When the GM tube fires, it's resistance can be treated as near zero for a moment. So another resistor divider to look at is the one formed by \$R_7\$ and \$R_6\$. Again, in theory, the LM358D doesn't appear to be exposed to high voltage because of this divider. But here again a single failure of \$R_7\$ might mean significantly otherwise.

There are lots of ways this circuit could and probably should be made a little more robust to single failures. But the parts are cheap and the voltage is low enough, I suppose.

Anyway, have fun. There is a lot to learn about GM tubes and what they respond to and what they cannot respond to, as well. In this case, I suspect (from old knowledge) that these are probably neon-chlorine mixtures. Possibly with an Argon admixture, I suppose, though the voltage will be slightly higher for that. Responses will probably only be due to gamma rays, my guess. But perhaps technology has changed a lot and I'd be interested in the exact tube you are considering here. If you can find a piece, I'd recommend getting a sample of Autunite for testing/playing. Beautiful crystals in some cases, too. And quite active.

The design and construction of GM tubes is an interesting area to study. I'd recommend using your goal here to motivate some study of them. Focus on the basic principles of operation, the problems related to quenching (solved either by external quenching circuitry or the admixture of gases to the tube for so-called self-quenching within the tube), and the problems related to lifetime (number of counts) and the choice of cylinder and rod materials in combination with gases to extend the useful life. There is much more: the ideas of "cross-section" (measured in Barns) and how that relates to the energy of the particles that may cause a response; particle cascades; the different kinds of particles; the idea of mica windows and other ways to increase sensitivity to certain particles or energies; etc. Much to be learned, tested, etc. Lots of fun ahead.